Wow - lots of replies and some really helpful thank you. I'm not naturally a very empathetic person and would naturally tend towards Blondes way of thinking
but I've been on enough management training/fluffy HR courses in my time to know that it's not always the best approach to just lay down the law. I also agree with Outraged that while it's irritating the hell out of me, sacking a very good nanny who has an excellent relationship with my children and is utterly reliable is a little OTT.
Couple of answers to questions:
Baby is mix fed due to weight and jaundice at birth, never got back to EBM. My approach has been to BF, then top up twice a day. She is now bottle fed either formula or EBM in the mornings but initially resisted the feeder rather than the food I think. She would battle the nanny, but if I turned up and tried, would accept it to everyone's irritation. Possibly picking up on tension - I take your point RosyRoo, it is difficult if the kids are kicking off regardless of how hands off the parents are. I'm using medela and tommy tippee but I don't think that the bottles are an issue. Our nanny just wants her to take in the full feed in one go and she is more of a snacker. We've altered the routine slightly so she has 170 ml after her early nap and another 100 just before the lunchtime nap and that seems to be working well.
Sling - a few people have mentioned this. It's been used a few times but she has some back problems and is not that keen. It's been soooo cold and windy here too that I've avoided it myself. It's a decent back support sling so changing it won't improve matters.
Swimming - I wouldn't take them both swimming personally. The toddler is due to start lessons on weekends so if they went well, she could in time but it's one child per adult in the interim.
There are tons of activities and groups in the area, and things to do. We live in a part of London with nice parks, open spaces and kid friendly cultural stuff [not Kensington sadly] so it's really not challenging to occupy them but perhaps she is just going through a bit of a rut on that front. Several of the groups are run from centres in parks or in areas where a toddler would have to go some distance to come to harm.
Our toddler (2.7months) is big for her age and walks everywhere but is still at that stage where she is prone to giving up/crashing out if you overdo things. I know that makes her nervous about having them both out at the same time but she is adamant about not reverting to putting the toddler into pram. Our nanny is quite short so can't manage to push the pram and the buggy board at the same time. I'm wondering if changing the pram to a Phil & Teds or similar will give her a bit more flexibility. Don't particularly want the vast expense to be honest but I will sound her out about it.
Routine - I'm not personally a Gina Ford afficionado. We certainly don't plan our lives around the routine at weekends and if I thought that either child was being left to cry it out for hours, I would sack her. That said, I do think that routine to some extent is a good thing and I've also found that most children will naturally fall into one so I don't think it harms anyone to be gently prodded into one. Baby whisperer and Gina Ford routines are not that dissimilar imo, just the methodology of implementing them from what I can see. Ultimately, I'm not the one at home all day so both my husband and I feel that it is deeply unfair to prescribe an in-loco parenting method that we don't have to work with. It's a long day to have two children with no structure to work towards
If I'm quite honest, our nanny could be described as quite high maintenance on a personal level and likes to be seen as the ultimate expert on all things child related. She is not enjoying being back on a learning curve and has run off with all my PFB (and now untouched) What to Expect the First Yr etc
. It's quite nice to be marginally more experienced in this phase 
She is quite strict about behaviour, and would be mortified to be sitting in a class or group with a toddler/baby playing up. She loves to tell me how my DD showed up other children/shone in some way. I suspect it has more to do with her inability to go with the flow and accept that things will not be perfect for a little while than much else. She has two nanny/friends who are the same nationality but with more badly behaved children and is quite happy to go on playdates to their homes and have the baby with her. Feeding a baby in a group environment though will force her to make conversation with other people rather than play with the toddler and I think she wants to avoid that at all costs. Probably why I would just bite the bullet and she does not. To be fair, there aren't a huge number of nannies in the area, despite the dire childcare on offer and she finds that once local mums find out she is a nanny, they tend to close down the conversation and move on. Horrid.
I had a couple of calls with work first thing so had to hand them over and run this morning, they haven't gone out again so I'll have to bite the bullet later today and insist that things change tomorrow. It's another beautiful day and they've had no fresh air. It's approximately 300metres to the park gate so I'm quite
. I wouldn't be happy going back to work at present and it needs to be sorted.